Covering relations for multidimensional dynamical systems
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Publication:1877848
DOI10.1016/j.jde.2004.03.013zbMath1061.37013OpenAlexW2048280869MaRDI QIDQ1877848
Marian Gidea, Piotr Zgliczyński
Publication date: 19 August 2004
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jde.2004.03.013
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Isolating blocks and symbolic dynamics
- Homoclinic phenomena in Hamiltonian systems with several degrees of freedom
- Fixed point index for iterations of maps, topological horseshoe and chaos
- Heteroclinic connections between periodic orbits in planar restricted circular three-body problem -- a computer-assisted proof
- Periodic orbits, symbolic dynamics and topological entropy for the restricted 3-body problem
- Isolating neighborhoods and chaos
- Computer assisted proof of chaos in the Lorenz equations
- Isolating segments, fixed point index, and symbolic dynamics
- Topological horseshoes
- A Chaos Lemma
- Computer assisted proof of chaos in the Rössler equations and in the Hénon map
- Positive Topological Entropy of Chua's Circuit: A Computer Assisted Proof
- A generalized Lefschetz fixed point theorem and symbolic dynamics in delay equations
- A generalization of the Lefschetz fixed point theorem and detection of chaos
- Sharkovskii's theorem for multidimensional perturbations of one-dimensional maps
- MULTIDIMENSIONAL PERTURBATIONS OF ONE-DIMENSIONAL MAPS AND STABILITY OF SARKOVSKĬ ORDERING
- TOPOLOGICAL ENTROPY FOR MULTIDIMENSIONAL PERTURBATIONS OF ONE-DIMENSIONAL MAPS
- Symbolic dynamics for the Hénon-Heiles Hamiltonian on the critical level
- On periodic points for systems of weakly coupled 1-dim maps.